Scaling of proposals for Metropolis algorithms is an important practical problem in MCMC implementation. Analyses of the random walk Metropolis for high dimensional targets with specific functional forms have shown that in many cases the optimal scaling is achieved when the acceptance rate is approximately 0.234, but that there are exceptions. We present a general set of sufficient conditions which are invariant to orthonormal transformation of the co-ordinate axes and which ensure that the limiting optimal acceptance rate is 0.234. The criteria are shown to hold for the joint distribution of successive elements of a stationary p-th order multivariate Markov process.